Higher correlation functions of the Ising ferromagnet. The case of a linear model for spin $S=1/2$

The Ising problem tor the spin $S\geqslant 1/2$ is solved by means of the two-time Green function method. It is shown that the chains of the coupled equations for Green functions are reduced to the closed systems of $L=2SP+1$ equations, $P$ being the coordination number of the lattice. The Green functions for $L=3,5,7,9,11$, found from these equations, make it possible to obtain sets of exact relationships for correlation functions. It is shown that these relationships lead to the complete solution of a dynamical problem in the case of a linear model $S=1/2$ (the two-particle and many-particle correlators are found) with various boundary conditions: the infinite chain of spins, the spin chain closed in a ring and the finite spin chain with fixed states of boundary spins.